Problem Solving With Venn Diagrams

In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games.

Find the total number of students in the group In a college, 60 students enrolled in chemistry,40 in physics, 30 in biology, 15 in chemistry and physics,10 in physics and biology, 5 in biology and chemistry. Find how many are enrolled in at least one of the subjects.

When he asked how many had been to Punta de las Cuevas, four children raised their hands.

When he asked how many had been to Salt Bay, three raised their hands.

Sometimes when I know the correct answer I can work backwards to solve it, but I can't do that with this problem. This sort of problem is often solved using a Venn diagram.

You can read about them at these locations: Wolfram Mathworld: Venn Diagram Venn Diagram: Fast Food Restaurants here's another way to organize the data you have and solve the problem. We're told that 3 students belong to both clubs: photography ~photography ------------ ------------ computer | 3 | | ------------ ------------ ~computer | | | ------------ ------------ Now, if 12 students belong to the computer club, and we've already accounted for 3 of them, there must be 9 who are in the computer club, but NOT the photography club, right?Puzzles involving two or three properties of people or objects, commonly solved by Venn diagrams, are popular with teachers, and perhaps not so popular with students!Several have asked about them recently, leading me to catalog our past answers about them, to find the most useful examples to point to.Let’s look at one more example with two sets, this one using a table rather than a Venn diagram.This is from 2009: Alternate Solution Path to Venn Diagram Problem There are 30 students in a math class. I know that the correct answer (according to the book) is 13. I have either 10 or 7 as my answers, not knowing if the "both club" members are included already in the listed number of members.Twelve belong to the computer club, and eight belong to the photography club. This question is listed in a section introducing proportions.I can't figure out a way to come up with the correct answer or use a proportion to solve it.In a town 85% of the people speak Tamil, 40% speak English and 20% speak Hindi.Also 32% speak Tamil and English, 13% speak Tamil and Hindi and 10% speak English and Hindi, find the percentage of people who can speak all the three languages.An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines.Also 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Find Let T, R and M represent the people who use Television, Radio and Magazines respectively.


Comments Problem Solving With Venn Diagrams

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